To set checkbox with a default value of checked and save the property as a Boolean property type in the JCR (rather than a String), use the following Classic UI settings:
<myCheckbox
jcr:primaryType="cq:Widget"
fieldLabel="My Checkbox"
name="./myCheckbox"
value="true"
defaultValue="true"
checkboxBoolTypeHint="{Boolean}true"
type="checkbox"
xtype="selection"/>
Or use the following settings in the Granite Touch UI:
<myCheckbox
jcr:primaryType="nt:unstructured"
sling:resourceType="granite/ui/components/foundation/form/checkbox"
text="My Checkbox"
name="./myCheckbox"
value="true"
checked="true"/>
<myCheckboxType
jcr:primaryType="nt:unstructured"
sling:resourceType="granite/ui/components/foundation/form/hidden"
name="./myCheckbox@TypeHint"
value="Boolean"/>
There's a detailed writeup and demo at http://www.nateyolles.com/blog/2015/11/aem-checkboxes-using-sling-post-servlet.